Rice: Wash the rice in several changes of water until the rinse water is no longer cloudy, drain well and place in a covered saucepan or rice cooker with water. Bring to a boil then reduce heat to a simmer and cover the saucepan. Allow the rice to simmer until the top looks dry; about 15 minutes. Turn off the heat and let stand for 10 minutes to absorb the rest of the water. Alternatively, you can use a rice cooker.

Mix the rice vinegar and sugar in a small bowl until the sugar has dissolved then stir the mixture into the cooked rice until well combined. Allow the rice to cool then set aside. To speed up the process, place the rice in the freezer. For faster cooling, spread the rice against the sides of the bowls for even distribution.

Roll:
Roll the sushi cover a bamboo rolling mat with plastic wrap. Lay a sheet of nori, shiny side down on the plastic wrap. With wet fingers firmly pat a thin even layer of prepared rice over the nori, leaving 6mm uncovered at the bottom edge of the sheet. Sprinkle the rice with about 1/2 teaspoon of sesame seeds and gently press them into the rice. Carefully flip the nori sheet over so the seaweed side is up.
Making an horizontal indent across the first quarter of the rice, spread the mayonaise and the wasabi across it. Following this, place 2 or 3 long cucumber spears, 2 or 3 slices of avocado and about 1 tablespoon of crab sticks in a line across the nori sheet about 6mm from the uncovered edge.

Pick up the edge of the bamboo rolling sheet then fold the bottom edge of the sheet up, enclosing the filling and tightly roll the sushi into a cylinder about 4cm in diameter.
Once the sushi is rolled wrap it in the mat and gently squeeze to compact it tightly.
Cut each roll into 2cm pieces with a very sharp knife dipped in water.